I'm experiencing a hard starting problem, especially when cold on a 1608 motor with an electric, trunk mounted fuel pump. It usually takes several bouts of 5-10 seconds of cranking for the engine to fire initially, but once it starts it restarts immediately. The fuel pump is usually fairly noisy ( a distinct whine can be heard when the motor's running from the trunk). However, while the motor is cranking and not starting, I don't hear it. Also it goes silent while the engine's running from time to time, but the noise comes back after awhile.
Is the pump failing? This is the first time I'm dealing with a carbed car's electric pump, how can I test it? The Haynes manual is very sketchy about it

Any help would be greatly appreciated! (Yes, the ignition and timing are within spec, they are not the cause for the hard start - there's no gas reaching the carb).